Crack Paths 2012

strength, thus leading to the possibility of partially or totally substituting conventional

shear reinforcement [e.g., 9-14]. This last aspect could be particularly effective in order

to lessen the congestion of reinforcement in the critical regions of R Cframed structures,

so leading to a more rational and efficient design, especially in seismic zones. In order

to correctly take into account the effective contribution provided by steel fibres in the

post-cracking structural response, the analysis of SFRCmembers should be carried out

by using proper constitutive models, different from those currently adopted for ordinary

reinforced concrete structures. To this scope, the 2D-PARCmodel, already developed

for R C elements subjected to plane stresses [15-16], has been also extended to SFRC

ones, by including a proper softening law [3] which takes into account the additional

transmission of tensile stresses across cracks arising from the bridging effect of fibres.

2D-PARCM O D EFLO RC R A C K ES FDRC O N C R E T E

The theoretical formulation of the adopted constitutive relation, which has been

originally developed for ordinary R Celements, can be found in details in [15]. In this

work, the main features of the model will be only briefly outlined, while the attention

will be primarily focused on the evaluation of the resistant contribution offered by steel

fibres in the composition of the material stiffness matrix.

Description of the model

The adopted model, which refers to a SFRCmembrane element subjected to general

plane stresses (Fig. 1), is based on a smeared-fixed crack approach.

In the uncracked stage, concrete and steel are treated like two materials working in

parallel, by assuming perfect bond between them, while fibre contribution is neglected.

Crack formation takes place when the maximumprincipal stress exceeds concrete

tensile strength; furthermore, crack pattern is hypothesised as fully developed with a

constant spacing am1 (Fig. 1a).

\

σ y

τ

fibres

\[

τ

τ

[\

\

[\

Q

Q

W

W

Y

ψ

ψ 1

1

τ f12

[

ω 1

D

V

σ

P

Z

σ

[

[

ω

1

σ f

σ f1

[

W

τ

\[

(a)

(b)

σ

\

Figure 1. (a) SFRCmembraneelement in the cracked stage: geometry and notations; (b)

kinematical parameters of the crack.

652